   Chapter 10.3, Problem 38E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# The monthly demand function for x units of a product sold by a monopoly is p =   8000   − x dollars, and its average cost is C ¯ = 4000 + 5 x dollars.(a) Determine the quantity that will maximize profit.(b) Determine the selling price at the optimal quantity.(c) Determine the maximum profit.

(a)

To determine

To calculate: The quantity that will maximize profit if the monthly demand function for x units of a product sold by a monopoly is p=8000x dollars, and its average cost is C¯=4000+5x dollars.

Explanation

Given information:

The provided information is:

The monthly demand function for x units of a product sold by a monopoly is p=8000x dollars, and its average cost is C¯=4000+5x dollars.

Formula used:

The total profit function is:

P(x)=R(x)C(x)

Where R(x)andC(x) are total revenue function and total cost function.

Calculation:

Consider the provided information,

The monthly demand function for x units of a product sold by a monopoly is p=8000x dollars, and its average cost is C¯=4000+5x dollars.

Total cost function can be written as:

C(x)=C¯x=4000x+5x2

Total revenue function can be written as:

R(x)=px=8000xx2

Demand function is defined as:

p=8000x

Now find out the profit function as:

P(x)=R(x)C(x)<

(b)

To determine

To calculate: The selling price at the optimal quantity if the monthly demand function for x units of a product sold by a monopoly is p=8000x dollars, and its average cost is C¯=4000+5x dollars.

(c)

To determine

To calculate: The maximum profit if the monthly demand function for x units of a product sold by a monopoly is p=8000x dollars, and its average cost is C¯=4000+5x dollars.

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